3,305 research outputs found
Nowhere Weak Differentiability of the Pettis Integral
For an arbitrary infinite-dimensional Banach space \X, we construct
examples of strongly-measurable \X-valued Pettis integrable functions whose
indefinite Pettis integrals are nowhere weakly differentiable; thus, for these
functions the Lebesgue Differentiation Theorem fails rather spectacularly. We
also relate the degree of nondifferentiability of the indefinite Pettis
integral to the cotype of \X, from which it follows that our examples are
reasonably sharp.
This is an expanded version of a previously posted paper with the same name
Comment on "Spin-1 aggregation model in one dimension"
M. Girardi and W. Figueiredo have proposed a simple model of aggregation in
one dimension to mimic the self-assembly of amphiphiles in aqueous solution
[Phys. Rev. E 62, 8344 (2000)]. We point out that interesting results can be
obtained if a different set of interactions is considered, instead of their
choice (the s=1 Ising model).Comment: Accepted for publication in Phys. Rev.
From weak to strong types of -convergence by the Bocce-criterion
Necessary and sufficient oscillation conditions are given for a weakly
convergent sequence (resp. relatively weakly compact set) in the
Bochner-Lebesgue space \l1 to be norm convergent (resp. relatively norm
compact), thus extending the known results for \rl1. Similarly, necessary and
sufficient oscillation conditions are given to pass from weak to limited (and
also to Pettis-norm) convergence in \l1. It is shown that tightness is a
necessary and sufficient condition to pass from limited to strong convergence.
Other implications between several modes of convergence in \l1 are also
studied
Geometry of Banach spaces and biorthogonal systems
A separable Banach space X contains isomorphically if and only if X
has a bounded wc_0^*-stable biorthogonal system. The dual of a separable Banach
space X fails the Schur property if and only if X has a bounded
wc_0^*-biorthogonal system
Toward a homogeneous set of transiting planet parameters
With 40 or more transiting exoplanets now known, the time is ripe to seek
patterns and correlations among their observed properties, which may give
important insights into planet formation, structure, and evolution. This task
is made difficult by the widely different methodologies that have been applied
to measure their properties in individual cases. Furthermore, in many systems
our knowledge of the planet properties is limited by the knowledge of the
properties of the parent stars. To address these difficulties we have
undertaken the first comprehensive analysis of the data for 23 transiting
planets using a uniform methodology. We revisit several of the recently
proposed correlations, and find new ones involving the metallicity of the
parent stars.Comment: 4 pages including figures. To appear in Proceedings of IAU Symposium
253, "Transiting Planets", May 2008, Cambridge, M
Clump stars in the Solar Neighbourhood
Hipparcos data has allowed the identification of a large number of clump
stars in the Solar Neighbourhood. We discuss our present knowledge about their
distributions of masses, ages, colours, magnitudes, and metallicities. We point
out that the age distribution of clump stars is ``biased'' towards
intermediate-ages. Therefore, the metallicity information they contain is
different from that provided by the local G dwarfs. Since accurate abundance
determinations are about to become available, these may provide useful
constraints to chemical evolution models of the local disc.Comment: 6 pages, proc. of the Sept. 20-24, 1999 Vulcano Workshop "The
chemical evolution of the Milky Way: stars vs. clusters", eds. F. Matteucci,
F. Giovanell
Lie Superalgebras and the Multiplet Structure of the Genetic Code II: Branching Schemes
Continuing our attempt to explain the degeneracy of the genetic code using
basic classical Lie superalgebras, we present the branching schemes for the
typical codon representations (typical 64-dimensional irreducible
representations) of basic classical Lie superalgebras and find three schemes
that do reproduce the degeneracies of the standard code, based on the
orthosymplectic algebra osp(5|2) and differing only in details of the symmetry
breaking pattern during the last step.Comment: 34 pages, 9 tables, LaTe
A new inverse method for stellar population synthesis and error analysis
The stellar population synthesis in unresolved composite objects is a very
tricky problem. Indeed, it is a degenerate problem since many parameters affect
the observables. The stellar population synthesis issue thus deserves a deep
and rigourous analysis. In this paper we present a method of inversion which
uses as observables the intensities at each pixel of a galactic spectrum and
provides the stellar contribution to luminosity of all stars considered in a
database. The main contribution of this paper to the synthesis problem is that
it provides an analytical computation of the uncertainties accompanying a
solution. This constitutes an important improvement relative to previous
methods which do not provide such infomation except in the method described by
Pelat (1997) and Moultaka & Pelat (2000). The latter uses the equivalent widths
and intensities of stellar spectra in order to reproduce the equivalent widths
of a galactic spectrum. The novelty of this work relative to the previous one
is that the dust emission present in the IR spectra can be modeled as well as
the velocity dispersion of stars that broadens the lines of a galactic
spectrum. Tests are also performed in order to estimate the reliability of the
method and the influence on the results of an additive continuum present in a
studied spectrum, for example in the case of AGNs.Comment: 12 pages, 4 figures, 7 tables. In press in A&
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